If I can take a more reserved approach, it is normal for LW to take some time to connect properly! After you open LW & the old dnlds are re-loaded, LW will search out for immediate sources for these files. Depending upon how many incomplete files you have, this can take several mins (Yu need to be patient.) If you have any forced 'resume' or should I say many, then this will have a definite affect on your connection quality (whilst you might dwld these files ok, you won't be able to search b/c your connection energy is drained upon the resumed files.) May I suggest you don't resume dwnlds unless absolutely necessary. Search & dwnld techniques can help :
Here's some search hints! Also remember that if you share a reasonable no. of files, you'll have a better chance of good connections & search results.